Related papers: Subsystem constraints in variational second order …
The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for…
Recent experiments have demonstrated direct cooling and trapping of diatomic and triatomic molecules in magneto-optical traps (MOTs). However, even the best molecular MOTs to date still have density $10^{-5}$ times smaller than in typical…
Nonlinear light-matter interactions and their applications are constrained by properties of available materials. The use of metamaterials opens the way to achieve precise control over electromagnetic properties at a microscopic level,…
We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem…
We consider diatomic systems in which the kinetic energy of the electrons is treated in a simple relativistic model. The Born-Oppenheimer approximation is assumed. We investigate questions of stability, deducing bounds on the number $N$ of…
Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest "atoms"? In the following paper we answer these…
When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
Motivated by the Penrose-Onsager criterion for Bose-Einstein condensation we propose a functional theory for targeting low-lying excitation energies of bosonic quantum systems through the one-particle picture. For this, we employ an…
In composite Higgs models the pseudo-Nambu-Goldstone Boson (pNGB) nature of the Higgs field is an interesting alternative for explaning the smallness of the electroweak scale with respect to the beyond the Standard Model scale. In…
Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence,connectivity and gate…
Electron charging play key roles in physiochemical processes, whose intrinsic stabilization in single molecules is desirable for tailoring molecular functionality and developing molecular devices, but remains elusive on surfaces. Here, we…
We study bosonic systems in the regime in which the two-body system has a shallow bound state or, equivalently, a large value of the two-body scattering length. Using the effective field theory framework as a guide, we construct a series of…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
In this paper we discuss constraints on two-dimensional quantum-mechanical systems living in domains with boundaries. The constrains result from the requirement of hermicity of corresponding Hamiltonians. We construct new two-dimensional…
This paper deals with the derivation of a collective model of cell populations out of an individual-based description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving…
In this paper, we introduce the second-order subdifferentials for functions which are G\^ateaux differentiable on an open set and whose G\^ateaux derivative mapping is locally Lipschitz. Based on properties of this kind of second-order…
We study the separability of bipartite quantum systems in arbitrary dimensions based on the Bloch representation of density matrices. We present two separability criteria for quantum states in terms of the matrices $T_{\alpha\beta}(\rho)$…
We consider spin systems between a finite number $N$ of "species" or "phases" partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases…